Let's see.

If I were "Michael", and Carlo, while married to my sister, set up my brother to be gunned down by an enemy, after which he continued for years to live off my family and would've gone on doing so and may have even fingered others down the line had his betrayal never been discovered....

Then no, I would not have let Carlo live. I would have had no problem standing Godfather to his newborn son while all the while planning his execution. The feelings of my sister Connie, much as I love her, would play absolutely no role in the murder of this weasel of a scumbag she married.

And for the record, 'if' I were "Michael"...I would not have let Fredo live, either.

Apple